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NON-COGNITIVE DEVELOPMENT IN EARLY CHILDHOOD: THE INFLUENCE OF

MATERNAL EMPLOYMENT AND THE MEDIATING ROLE OF CHILDCARE

DRAFT WORKING PAPER

Thérèse McDonnell

ABSTRACT

This paper examines the relationship between maternal employment during infancy and the

non-cognitive development of pre-school children. Non-cognitive skills, such as personality

traits, character, goals, motivations and preferences, are at least as important as cognitive

skills for personal development and later labour market success.

Drawing on recent advances in the economics literature on the theory of skill formation, this

study uses data on Irish pre-school children (Growing Up in Ireland, Infant Cohort) to

examine the influence of maternal employment in early childhood on non-cognitive skills.

Propensity score matching addresses the issue of potential selection bias and mediation

analysis is used to investigate possible mechanisms for the effect of maternal employment,

in particular the role of childcare, parental stress, quality of parent-child attachment and

income.

Full-time maternal employment in early childhood has a significant and detrimental effect

on the non-cognitive development of pre-school children from less advantaged

backgrounds, as measured by maternal education. This effect is primarily mediated by

childcare choice, such that many children in informal childcare at 9 months old, particularly

unpaid grandparental arrangements, are more likely to have behavioural difficulties, as

defined by the Strengths and Difficulties (SDQ) score, at 3 years old. While parent-child

attachment has a modest role in this effect, income and parental stress do not explain the

effect of maternal employment for these children. When selection on observables is used to

assess bias arising from selection on unobservables, maternal employment estimates are

determined to be a lower bound.

Key words: non-cognitive skills, socio-emotional, maternal employment, childcare.

Thérèse McDonnell would like to acknowledge the scholarship funding received from the

Department of Children and Youth Affairs, Ireland.

Corresponding author: Thérèse McDonnell therese.mc-donnell@ucdconnect.ie.

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1.1 INTRODUCTION

Female labour force participation among childbearing aged women has risen sharply in most

OECD countries, with average participation rates increasing from 54 percent in 1980 to 71

percent in 2010 (OECD Statistics on Employment). Research that contributes to an

understanding of the impact of this phenomenon on child wellbeing is important both to

help parents make appropriate parental investment decisions and for policy makers to

ensure families are supported in a manner that protects child development. As an increase

in the provision of childcare services has been both a response to and a driver of this

increased female labour force participation (Thévenon, 2013), an examination of the role

played by childcare choices on child development is critical to a comprehensive analysis of

the effects of maternal employment.

This study focuses on the influence of maternal employment on the development of non-

cognitive skills in early childhood. Non-cognitive skills, personality traits that are weakly

correlated with measures of intelligence, are at least as important as cognitive skills for

personal development and later labour market success (Brunello & Schlotter, 2011). The

Five – Factor Model offers a definition of these personality traits: agreeableness,

conscientiousness, emotional stability, extraversion and autonomy (Nyhus and Pons, 2005).

While individuals with higher levels of cognitive and non-cognitive skills make a positive

contribution to society, a variety of problems, such as crime, obesity, and teenage

pregnancy, can be attributed to low skill levels (Heckman et al., 2010; Knudsen et al., 2006;

Carneiro et al., 2007). Inadequate development of these skills during the sensitive period of

early childhood may manifest as behavioural problems, which in turn may signal difficulties

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later in life. For example, early aggression has been shown to predict criminality and

violence in adulthood (Nagin & Tremblay, 1999), and social maladjustment in childhood is a

strong predictor of educational attainment and career advancement (Silles, 2010).

The need to consider non-cognitive development is highlighted by studies of early

intervention programs, which identify early childhood as a critical period in child

development (Heckman et al., 2010). Indeed, these studies demonstrate that non-cognitive

skills may be more malleable in the long-term to early intervention than cognitive skills.

Given the brain is most flexible early in life, (Centre on the Developing Child at Harvard

University, 2007), this early plasticity means it is more effective to influence the developing

brain architecture during infancy than in adulthood. Therefore, while an understanding of

the factors that influence the development of non-cognitive skills in early childhood is

crucial to supporting healthy development, it also has the potential to inform policy

decisions over many domains including education, health and justice.

This study uses data on Irish pre-school children to examine the relationship between

maternal employment when a child is 9 months old and non-cognitive skills at age 3, as

measured by the Strengths and Difficulties Questionnaire (SDQ). Mediation analysis

investigates non-parental childcare, parental stress, income and quality of mother-child

attachment as mechanisms that may channel the effect of maternal employment on non-

cognitive development.

1.2 Maternal Employment – Potential Mediators

There are a number of mechanisms through which the influence of maternal employment

on child development may be manifested. Non-parental childcare replaces maternal care

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with that of another caregiver, and may also expose a child to a new environment. This is

important as evidence suggests that early environmental conditions directly affect the

expression of genes that control the development of the brain and the nervous system

(Weaver et al., 2004). A key feature during this early developmental process is the “serve

and return” relationship between children and their parents and other caregivers. This

refers to the back and forth non-verbal interactions between an infant and caregiver (Centre

on the Developing Child at Harvard University, 2007). The absence of appropriate sensitive

interactions can result in deficits in the brain’s architecture, which in turn leads to

disparities in learning and behaviour. More specifically, the quality of the care relationships

a child is exposed to in the early years, be they maternal, paternal or non-parental, can

directly influence the child’s response to stress, as expressed by the epigenomic state of a

gene (Weaver et al., 2004).

Parent-child attachment is another channel through which maternal employment may

influence a child’s development. The purpose of attachment is to make a child feel safe,

secure and protected (Benoit, 2004), and low levels of attachment in early childhood can

result in long term problems. For example, children raised in institutional care have been

found to exhibit low levels of attachment security to their primary caregiver (Almas et al.,

2012), experience more social problems later in life (Erol et al. 2010), and report no specific

friendships (Roy et al., 2004). While a child’s experience in institutional care does not

compare with the experience of non-parental childcare, these findings clearly illustrate that

secure attachment is fundamental to the healthy development of a child.

Balancing the dual role of mother and employee may prove stressful for many employed

mothers (Chatterji et al., 2011). As parental stress has been associated with adverse

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outcomes for children including insecure attachment and behavioural problems (Crnic and

Low, 2002), stress may act as a mediator for the effects of maternal employment on non-

cognitive skill development. However, McBride (1990) suggests each of these roles provides

a context for social interaction and feedback valued by women, which may offset the

potential stresses of increased time and energy demands.

A final mediator for the effect of maternal employment on non-cognitive skills is income.

Recent research has highlighted the role of family income in the formation and evolution of

children’s non-cognitive skills (Fletcher & Wolfe, 2012). Becker and Lewis (1973) show that

greater family resources typically lead to a greater investment in children, increasing the

marginal cost of children. Higher income may lead to fewer children and a higher standard

of living for the family, with access to better health services, education, nutrition, and

recreational activities. Maternal employment increases the financial resources within a

family and therefore may lead to greater levels of investment in a child, which in turn may

facilitate the development of non-cognitive skills.

1.3 The contribution of this study

This study contributes to this field in a number of areas. Firstly, much of the research on

maternal employment/childcare and non-cognitive skills of children emanates from the

USA. However, with country specific factors such as maternity leave entitlements, supports

for working parents, and the extent and quality of childcare services, likely to exert an

influence on child development, research from other countries makes a valuable

contribution. Secondly, much of the economics literature has primarily focused on the

influence of maternal employment and childcare on the development of cognitive skills. Yet,

following the seminal work of Heckman et al., (2007), attention has now been drawn to non-

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cognitive skills. This study adds to this emerging, but as yet, relatively modest body of

literature. Thirdly, many of the studies in this field utilise data on children born over 20

years ago (e.g. Gregg et al., 2005; Baker et al., 2005; Lefebvre et al., 2000; Gupta et al.,

2010), while the present study utilises data from the infant cohort of the Growing Up in

Ireland study, which gathers data on children born between 1 December 2007 and 30 June

2008. The nature of maternal employment and childcare has evolved substantially, thus this

recent data reflects current circumstances. Fourthly, this study has certain methodological

strengths that underpin the robustness and validity of its findings. Propensity score

matching reduces potential selection bias by yielding a cohort that is balanced in respect of

measured covariates. Mediation analysis helps to understand the factors that may channel

the effects of maternal employment on non-cognitive skills. The calculation of a ratio that

determines how large the selection on unobservables would need to be in order to attribute

the entire effect of maternal employment to selection bias (Altonji et al., 2005) allows the

reader to interpret the robustness of results to the threat of selection bias.

2. THEORETICAL MOTIVATION AND LITERATURE

2.1 Theoretical Framework

Building on evidence developed within the field of epigenetics and studies of a number of

early intervention programmes (in particular Abecedarian, Perry Preschool and Chicago

Child-Parent Centre interventions), Heckman et al. (2007) have developed a body of work

which highlights the role of early environmental conditions in the evolution of cognitive and

non-cognitive skills. Their theory of the technology of skill formation states that capabilities,

both cognitive and non-cognitive, are produced by investments, the environment, and

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genes. The capability formation process comprises a number of related developmental

stages, each of which corresponds to a period in the child’s lifecycle. Stages are linked such

that inputs in one period produce outputs, which represent changes in capabilities, at the

next period. Sensitive periods are stages that are more effective in producing certain

capabilities, while critical periods are stages that alone are effective in producing a

capability. Capabilities are self-reinforcing and cross-fertilising, defined as “self-

productivity”. Capabilities produced at one stage of the lifecycle increases the productivity

of investment at later stages, and levels of investment in capabilities at different ages

bolster each other, a process labelled as “dynamic-complementarity”.

The production function of capability formation, assuming a constant elasticity of

substitution, has a vector of the adult stock of capabilities as the output, and includes two

important variables:

Ø is the complementarity measure, which measures how well inputs in later periods

substitute for inputs in earlier periods, with Ø = 1 meaning investments in each

period are perfect substitutes, and Ø approaching - ∞ meaning investments are

perfect complements. The smaller Ø the less effective later investment is in

producing skills.

ɣ is the capability multiplier, which boosts skill output through increasing the

production of skills in the current period (self-productivity), and increasing Ø, thus

raising the productivity of investment in later periods.

However, the timing of investment must also take r, the interest rate, into account. Using a

two period model where investments in either period are perfect substitutes (Ø = 1), the

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interest rate and the capability multiplier have opposing influences. The higher the

capability multiplier the greater the value of early investment, yet the higher the interest

rate, the greater the preference to delay investment. A utility maximising parent will only

invest in their children early in the lifecycle if ɣ > (1 - ɣ)(1 + r). Should Ø approach - ∞, such

that investments in each period are complements, then earlier investment is optimal and

the skill multiplier plays a minor role. Estimating this model using the National Longitudinal

Survey of Youth, Heckman et al. (2010) conclude that there is no evidence of the

malleability or substitutability for cognitive skills later in life, while the malleability for non-

cognitive skills appears consistent between life stages. Applying these findings to the design

of interventions to counteract disadvantage suggests that intervention programmes

targeting early childhood are likely to be more beneficial, as both cognitive and non-

cognitive skills can be improved (dynamic-complementarity), and cognitive skills can be

further boosted by higher levels of non-cognitive skills (self-productivity).

Maternal employment in the early years may allow for greater investment in a child,

particularly if maternal employment is well paid. However, this greater financial investment

may result in a reduction in the investment of maternal time. The impact of this time

constraint may depend on both the nature of replacement childcare and the quality of the

mother-child relationship. Grossman (1972), in his seminal work "On the Concept of Health

Capital and the Demand for Health", states that greater education should make an

individual more efficient at producing health. Cutler & Lleras-Muney (2006) state that

education can affect behaviour and decision-making. For example, education may affect

health through lower future discount rates, such that the more educated may place a higher

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value on the future (Becker & Mulligan, 1997). Therefore, maternal education should play

an influential role in the production of skills in childhood.

2.2 Literature

Within the field of economics, empirical research on the influence of maternal employment

and childcare on child outcomes has primarily focused on cognitive development (e.g. Ruhm

2004; Vandell and Ramanan, 1992; Gregg et al., 2005). However, some recent research has

examined non-cognitive development. A key challenge within this literature is the ability to

establish a causal relationship between maternal employment/non-parental childcare use

and child wellbeing. If parents who work and/or use non-parental childcare differ from

those that do not in ways that may influence the non-cognitive development of the child,

then the estimated effects may be biased by these unobserved traits. Therefore, studies

that address this problem are likely to produce more robust results.

Relying on a rich set of control variables to address potential unobserved selection bias and

controlling for childcare type and intensity, del Carmen Huerta et al. (2011) use ordinary

least squares (OLS) and logit estimators to examine data from five OECD countries.

Assessing the impact of the timing of a mother’s return to employment on both cognitive

and behavioural development, the authors find that British children of mothers who

returned to work within 6 months of the child’s birth are more likely to experience

behavioural problems, though the effect sizes are modest. However, no such pattern

emerges for the other countries (Australia, Canada, United States and Denmark). Formal

childcare and pre-school participation in some countries is associated with poorer

behavioural outcomes, yet the associations are small but long-lasting. The authors conclude

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that maternal employment is only one factor influencing child development, and that formal

childcare participation and parenting activities often have a greater influence on child

outcomes.

Exploiting the quasi-experimental opportunity provided by the introduction of a subsidised

childcare programme in Quebec, Baker et al. (2005) use a difference-in-difference estimator

to investigate the impact of this policy on labour supply, childcare utilisation and outcomes

for both children and parents in two parent families. They find that subsidised childcare

increases both female labour supply and, to a lesser extent, childcare usage as some

childcare moved from informal to formal arrangements. However, this policy change

resulted in poorer outcomes for children in terms of behaviour and health, led to less

consistent parenting, poorer family relationships and worse parental health. Kottelenberg &

Lehrer (2014) use both difference-in-difference and change-in-change (Athey and Imbens,

2006) estimators to investigate whether the negative findings of Baker et al. (2005) vary by

the age of entry into childcare. They find that early enrolment has a negative impact on

motor-social developmental scores, parental report of child health, and behavioural

outcomes, with the exception of hyperactivity and inattention scores, which have a negative

relationship for entry at age 4, though not at an earlier age. This study suggests that the

timing of both entry to and use of childcare matters.

Instrumental variable (IV) techniques can prove effective in isolating selection bias. As a

suitable instrument must be correlated with the explanatory variable and not with the error

term in the explanatory equation, the challenge of finding such an instrument means that IV

techniques are rarely applied in this field. Nonetheless, two studies to date have identified

appropriate instruments. Using access to kindergarden based on the level of state spending

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on pre-kindergarden programmes as an instrument, Magnuson et al. (200) apply an IV

estimator to US data and find that formal childcare prior to kindergarten entry results in a

greater degree of behavioural problems on entering school. Also using an IV approach,

Gupta and Simonsen (2010) use variation in the level of guaranteed access to the provision

of municipally provided preschool as an instrument to assess the impact of childcare at age

3 on outcomes at age 7 in Denmark. They find that family day care usage, referring to care

by a childminder in their own home, compared with home care by a parent is associated

with higher difficulties scores for boys with mothers with low levels of education, but find

no such effect for formal childcare. As Baker et al. (2005), Kottelenberg & Lehrer (2014) and

Magnuson et al. (2004) all use North American data, institutional factors may explain the

variation in effects for formal childcare.

Studies from other disciplines also support the conclusion that the age of entry into

childcare is important. A number of studies conclude that childcare in the first 12 months is

associated with more behavioural problems such as externalising problems (Jacob, 2009;

Belsky, 2001; NICHD ECCRN, 2003), while formal centre-based care at the age of 3 or 4 is

associated with better behavioural outcomes in the early stages of schooling (Sylva et al.,

2004). Comparing informal care with formal care at 9 months, Hansen and Hawkes (2009)

find that children cared for by grandparents have higher difficulty scores. Psychologists

Lombardi & Colley (2014) utilise propensity score weights to investigate links between the

timing of return to maternal employment following child birth and cognitive and

behavioural skills at school entry. They find no association, with the exception of improved

cognitive skills for employment prior to 9 months and lower conduct problems for

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employment begun between 9 and 24 months. This study also investigates if maternal time,

stress and wages play a mediating role and find no evidence in support of this.

The impact of maternal employment and childcare on the non-cognitive skills of children is

likely to vary by demographic characteristics such as family structure, parental education,

and family income. A substantial literature has focused on the effect of childcare programs

on disadvantaged children, with most finding that high quality interventions in early

childhood improve the social, emotional and behavioural outcomes of young children

(Zagel, 2003; Knudsen et al., 2006). For children of lone mothers, non-parental childcare,

formal or informal, for at least 25 hours per week has been found to be beneficial (Zagel et

al., 2013). However, maternal employment has resulted in poorer outcomes for children

from more advantaged backgrounds (Ruhm, 2008). As the effect of maternal employment

and childcare is likely to be heterogeneous, this study places a particular emphasis on the

disparity of outcomes for children of mothers with varying levels of education, primarily due

to the expectation that higher levels of maternal education should facilitate greater non-

cognitive development in childhood.

3. DATA AND METHODOLOGY

3.1 Growing Up In Ireland

This study uses data from the Infant Cohort of the Growing Up in Ireland study. The 11,134

participant children were selected randomly from the 41,185 children born between 1

December 2007 and 30 June 2008 as per the Child Benefit Register. This study uses data on

participants who responded to both wave 1 (sample size of 11,134), when the child was 9

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months, and wave 2 (sample size of 9,793), when the child was 3 years of age. Population

weights are used, where appropriate, to account for between wave attrition.

3.2 Non-Cognitive Skills – Strengths & Difficulties Score (SDQ)

Non-cognitive skills are measured using the score derived from the Strengths and Difficulties

Questionnaire (“SDQ score”) at age 3. This questionnaire is a parent completed instrument,

widely used to assess child socio-emotional behaviour (Goodman, 1997). The questionnaire

comprises of 25 items, covering five domains of behaviour: hyperactivity, emotional

symptoms, conduct problems, peer problems and pro-social behaviour. Each item has a

choice of one of three response categories – “not true” (0), “somewhat true” (1) and

“certainly true” (2). A total difficulties score is calculated from the addition of the scores for

the first 4 domains i.e. excluding pro-social behaviour. A score of 17 or greater is defined by

Goodman (1997) as abnormal or “problematic”, while a score of 14 to 16 is classified as

“borderline”. In this study, 4.4% of children can be described as problematic, while a further

7.1% fall within the borderline category. For the purpose of this analysis a child with a score

of 14 or greater is seen to be at risk, and is described as having a high SDQ score.

3.3 Maternal Employment

Utilising self-reported work status when the child is 9 months old, maternal work status1 is

categorised as home-duties (39%), part-time employment (21%), full-time employment

(27%), and mothers on leave but planning to return to work (13%). Binary variables are

constructed from these classifications for both the mediation analysis and propensity score

matching. Additional maternal employment covariates include a binary indicator of

1Maternal Employment: Home-duties (3,693), which includes those unemployed (292) and on long term illness (59); part-time (1,946),

includes those on state training schemes (42); full-time (2,582), includes full-time students (142); and with the fourth category relating to mothers on leave but planning to return to work (1,252).

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unemployment at 9 months, whether the mother worked prior to this birth and the average

hours worked pre-birth are treated as baseline covariates for estimation purposes. Maternal

employment status at 3 years, categorised as at home, part-time, full-time and maternity

leave, is also controlled for.

3.4 Choice of Baseline Covariates

Baseline control variables, as detailed in Table 1, are selected based on their theoretical

relevance, availability in the dataset, and the findings of prominent studies in the field. Child

and birth characteristics include gender, health at birth and at 9 months, whether the study

child was born prematurely, is a non-singleton, birth by caesarean section, and child

temperament at 9 months. Family characteristics include the household class, number of

siblings, an indicator of mother’s partner residing in the home, marriage quality score, rural

location, deprivation level of area of residence, whether the child and mother live with

grandparents, level of family support, whether family live close by, and receipt of social

welfare. Maternal characteristics include maternal smoking, drinking and drug taking during

pregnancy, her age when her first child was born and her age at Wave 1, ethnicity, and

whether or not she lived in a household at the age of 16 that experienced financial

difficulties. Also included are categories for the work status of the father at 9 months and 3

years and the father’s education level. Due to the extent of missing data on fathers,

indicator categories are utilised to signify missing data, ensuring the sample size is not

compromised. However, as a robustness check, multiple imputation is also utilised to

impute these missing variables.

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Baseline covariates also include variables identified as potential mediators measured at 9

months, with the exception of childcare and income variables, due to multicollinearity

concerns.

3.5 Potential Mediators

All potential mediators are selected due to their prominence in the literature on child

development. Mediation analysis assesses the role of these variables both at 9 months and

3 years.

3.5.1 Childcare

The majority (94%) of children who are in childcare at 9 months have a mother who is

employed. Yet, 31 percent of children with working mothers are cared for at home by a

parent. As there is no measure of childcare quality in the data, childcare type is used as a

proxy for quality, where the reference category is children cared for at home by their

mother or in childcare for 8 hours or less per week (60%). The second category includes

“Informal” care and comprises of children cared for by a childminder, relative other than a

grandparent, or friend in either the child’s or carer’s home (15%); the third category refers

to children cared for by a grandparent (14%), with the final category referring to children

cared for in a centre-based setting, which is labelled “Formal” care (11%). A further variable

indicaties whether or not the childcare is paid, and may also serve as a proxy for quality.

Finally, the number of hours in childcare is also controlled for. All childcare variables are

also measured at 3 years old.

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3.5.2 Quality of Attachment Score/Parent-child relationship

The ‘Quality of Attachment’ subscale uses 9 of the 19 items from the full Maternal Postnatal

Attachment Scale (Condon & Corkindale, 1998). When the child is 9 months, mothers are

asked about their feelings towards their infant and about themselves as parents. Response

categories for each question varies between three and five but all are re-scored to range

between one and five before calculating a total score. At 3 years of age, the Pianta CPR-S is

used, a fifteen-item measure that reflects both positive and negative aspects of the parent-

child relationship. It produces a Positive Aspects subscale and a Conflicts subscale.

3.5.3 Income

Equivalised family income in quintiles at both 9 months and 3 years of age is investigated as

a possible mediator. This relates to the income of the household from all sources, including

employment and social welfare payments, adjusted for the number of people in the

household. As income is endogenous to working, these variables are utilised only in the

mediation analysis.

3.5.4 Stress

The Parental Stress Scale, assessed when the child is 9 months, is a self report scale used to

mesaure positive and negative aspects of parenthood. It comprises a Total Parental Stress

Score as well as four subscales: Parental Rewards (6 items); Parental Stressors (6 items);

Lack of Control (3 items); and Parental Satisfaction (3 items). At three-years only the

Parental Stressors subscale was asked and this study focuses on the responses provided by

the mother as the primary caregiver.

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3.6. Methodology

Initially using the baseline covariates, Ordinary Least Squares (OLS) and Probit regression

analysis are used to examine the impact of maternal employment on the SDQ score and

likelihood of the study child having a high SDQ score (>=14) and propensity score matching

is utilised to address selection bias. Results are divided into sub-groups based on low (42%)

and high (58% - minimum of post-secondary school qualification) maternal education.

Mediation analysis is then applied, assessing each of the potential mediators individually, to

understand how any identified effects are channelled.

3.6.1 Propensity Score Matching

As maternal employment and child outcomes may be influenced by endogeneity, propensity

scare matching (PSM) is used to reduce any potential bias. PSM has the advantage of being

intuitively easy to understand, while also making no assumption on the functional form of

the relationship between the outcome and covariates (Dehejia and Wahba, 1999). Those

who receive a treatment i.e. maternal employment, are matched with those that do not

receive a treatment but have a similar probability of being treated based on observable

characteristics. Note that this approach does not address selection on unobservables,

therefore causal estimates may not be produced using PSM. This claim can only be made if

selection is on observables only or, in the case where unobservable characteristics influence

the selection into maternal employment, the balancing on observables also balances on

these unobservables.

Variables that are not affected by participation in the treatment (Caliendo and Kopeinig,

2005) are used in the estimation of the propensity score. These variables are then evaluated

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to assess the quality of the matching process, with a maximum standardised difference

between the two groups of 5% often deemed acceptable. The standardised difference is the

absolute difference in sample means divided by an estimate of the pooled standard

deviation of the variable. Variables with a difference substantially greater than 5% are

excluded from the final estimation of the propensity score in order to ensure comparability.

Once the propensity score is calculated, radius matching with a caliper (distance) of 0.01 is

used to match the treated with the control group. With the exception of nearest neighbour

without replacement, results are robust to the choice of matching estimator and caliper.

Each treated observation is matched with all counterfactuals within the caliper, with each

counterfactual observation within the calliper weighted equally. An untreated observation

may be matched with more than one treated observation and, while all treated

observations within the area of common support are matched, this may not be the case for

all observations in the control group. Appendix 4 details the selection of matching estimator

and the results of tests of the level of bias after each estimation.

3.6.2 Mediation analysis

A variable functions as a mediator to the extent that it accounts for the relationship

between a predictor and a dependent variable (Baron and Kenny, 1986). For example,

childcare may explain the effect, either partially or entirely, of maternal employment on the

SDQ score. In order to function as a mediator, a mediator variable must meet 4 conditions,

as detailed by Baron and Kenny (1986):

1. The independent variable (maternal employment) significantly affects the

dependent variable (SDQ scores) in the absence of the mediator (childcare),

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2. Variations in the level of the independent variable (maternal employment),

significantly account for variations in the mediator (childcare) - Path a;

3. Variations in the mediator (childcare), significantly account for variations in the

dependent variable (SDQ score) – Path b;

4. When the mediator (childcare) is controlled for, the previously significant

relationship between the independent variable (maternal employment) and the

dependent variable (SDQ score) is no longer significant – Path c. When this

coefficient is reduced to zero, this is strong evidence for a single dominant mediator.

Otherwise, there may be many mediators.

Multicollineratory of maternal employment and childcare may be a concern when both

variables are included in a regression, resulting on a reduction in the power of the test for

significance. Therefore, Baron and Kenny (1986) advise that it is important to examine both

the significance and the absolute size of these coefficients.

The Sobel-Goodman Test (Sobel, 1983) examines whether a mediator carries the influence

of an independent variable to a dependent variable and provides an approximate

significance test for the indirect effect of the independent variable on the dependent

variable via the mediator:

The standard errors for path a and b are and 2.

2 The exact formula, given multivariate normality for the standard error, includes

. However, this term is

ordinarily small.

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Variables that are not mediators may act as moderators, such that the effect of the

independent variable may vary by subgroups as defined by these moderators (for example,

education). However, some variables may act as confounders, influencing both the

independent variable and the outcome. Therefore, all baseline covariates are controlled for

in the mediation analysis.

a b

c

4. RESULTS

4.1 Descriptive Statistics

Descriptive statistics by maternal work status at 9 months are presented in Table 13. The

mean SDQ score is lowest for children of mothers working full-time and those on leave.

However, of greater concern is the probability of a high SDQ score, and children in these

categories also have a lower probability of a high SDQ score. However, there are a number

of key differences between these groups that must be accounted for in order to ascertain

the real effect of maternal employment.

3 A more detailed table is presented in Appendix 1.

CHILD CARE TYPE

(MEDIATOR)

MATERNAL EMPLOYMENT

(INDEPENDENT VARIABLE)

HIGH SDQ SCORE

(DEPENDENT VARIABLE)

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Full-time working mothers have the highest level of educational attainment, are more likely

to be from a household classified as professional/managerial, have fewer children, are older

when they have their first child, have a lower incidence of depression and have the highest

average equivalised household income, which may be expected as income is endogenous to

working. Mothers on home-duties have the highest rate of smoking, single parenthood and

chronic illness. They are also most likely to have lived in a family that had difficulty making

ends meet when they were aged 16.

22

TABLE 1 - DESCRIPTIVE STATISTICS SPLIT BY MOTHER'S EMPLOYMENT STATUS AT 9 MONTHS

ALL HOME PART-TIME FULL-TIME ON LEAVE

N 9751 3802 1994 2650 1272

% 39% 20% 27% 13%

SDQ score 7.79 8.31 7.71 7.35 7.24

SDQ score >=14 12% 14% 11% 9% 9%

Potential Mediators

Child Care at 9 months

At home with Mother 60% 95% 30% 18% 87%

Informal 15% 2% 28% 29% 6%

Grandparent 14% 2% 28% 26% 4%

Formal 11% 2% 15% 27% 4%

Childcare paid at 9 months 31% 3% 50% 68% 9%

Childcare hours at 9 months 10.61 0.70 14.00 26.41 2.26

Child Care at 3 years

At home with Mother 49% 72% 39% 27% 40%

Informal 15% 5% 20% 24% 18%

Grandparent 9% 3% 14% 14% 9%

Formal 27% 20% 28% 35% 33%

Childcare hours at 3 years 12.9 5.5 13.4 21.9 15.6

Childcarepaid at 3 years 45% 24% 52% 65% 54%

Equivalised Household Income at 9 months 21,839 16,309 22,215 27,491 25,624

Maternal Quality of Attachment 9 months 42.55 42.78 42.55 42.17 42.68

Maternal stress at 9 months 14.61 14.98 14.33 14.30 14.57

Equivalised Household Income at 3 years 18,334 14,408 18,644 22,121 21,522

Parent child relationship at 3 years - Positive score 33.80 33.72 33.81 33.88 33.86

Parent child relationship at 3 years - Conflict score 15.60 15.96 15.57 15.17 15.16

Maternal stress at 9 months 12.35 12.72 12.19 12.31 12.13

Workstatus at 3 years

At Home 42% 77% 20% 13% 31%

Part-time 28% 14% 59% 23% 34%

Full-time 23% 6% 15% 54% 23%

Maternity leave 6% 2% 7% 10% 11%

Non-Irish Ethnicity 19% 26% 14% 15% 12%

Age at first pregnancy 27.2 25.6 27.4 28.2 29.3

Age when study child is 9 months 31.9 31.3 32.2 31.8 33.5

Maternal Education

Up to leaving Certificate 43% 60% 41% 28% 29%

Degree Level 38% 30% 41% 44% 44%

Postgraduate 19% 10% 18% 28% 27%

Chronic illness (Mother) 11% 15% 9% 8% 12%

No. of siblings at 9 months 0.99 1.28 0.96 0.63 0.90

Household Class

Never worked 10% 23% 1% 4% 0%

Unskilled & Semi-skilled 9% 15% 8% 5% 5%

Skilled & Non-manual 30% 32% 35% 24% 27%

Professional/Managerial 51% 30% 56% 68% 68%

Partner 89% 83% 14% 94% 94%

23

4.2 Regression Analysis 4

Table 2 reports the results from both OLS regressions estimating the impact on the SDQ

score of maternal employment and probit regressions estimating the probability of a child

having a high SDQ score (>=14). While none of the employment categories are significant at

the aggregate level, when split by low and high maternal education, full-time maternal

employment has a negative and statistically significant effect on SDQ scores for children

with mothers with higher levels of education. A similar significant effect is found for children

of mothers who describe themselves as employed but have yet to return to employment.

The lack of a statistically significant effect from the marginal effects probit model for this

subsample suggests that these children are not at a greater risk of a high SDQ score. In

contrast, children of mothers with low levels of education that work full-time at 9 months,

have a 5% increased likelihood of a high SDQ score. However, the effect of maternal

employment at 3 years on the children of these mothers with lower levels of education is

favourable, with both part-time and full-time employment reducing the likelihood of a high

SDQ score, suggesting that the timing of maternal employment does matter.

While there are no significant findings for children of well educated mothers in

employment, household class plays a confounding role, such that maternal employment is

significant and favourable when household class is not controlled for. However, household

income is not significant for either subsample. This suggests that the home environment, in

particular parental social capital and ability, has a greater effect on non-cognitive

development than maternal employment.

4 Multiple imputation was carried out with equivalised income, parental stress, quality of attachment,

maternal depression, maternal drinking and drug taking while pregnant initially imputed. A further imputation was then carried out, adding Father’s education and workstatus to the variables imputed. Neither specification altered the size of the maternal employment coefficients, though part-time employment at 9 months for the low education subsample is significant at the 10% level under the latter specification.

24

TABLE 2 - OLS AND PROBIT (MARGINAL EFFECTS) RESULTS SPLIT BY EDUCATION

TOTAL SDQ SCORE (OLS) PROBABILITY OF SDQ SCORE >=14 (PROBIT)

ALL

LOW

MATERNAL

EDUCATION

HIGH

MATERNAL

EDUCATION ALL

LOW MATERNAL

EDUCATION

HIGH MATERNAL

EDUCATION

N 8,858 3,695 5,163 8,858 3,695 5,163

Maternal Workstatus at 9 months (versus at home)

Part-time Employment 0.135 0.338 -0.212 0.015 0.039 -0.008

[0.186] [0.296] [0.220] [0.013] [0.025] [0.012]

Full-time Employment -0.0305 0.356 -0.465** 0.015 0.051* -0.008

[0.187] [0.318] [0.221] [0.013] [0.027] [0.012]

On Leave -0.0531 0.391 -0.520** -0.001 0.006 -0.012

[0.190] [0.328] [0.218] [0.014] [0.026] [0.012]

Maternal Workstatus at 3 years (versus at home)

Part-time Employment -0.112 -0.191 0.0272 -0.022** -0.035** -0.007

[0.153] [0.249] [0.173] [0.010] [0.018] [0.010]

Full-time Employment -0.179 -0.491 0.0243 -0.027** -0.063*** -0.001

[0.168] [0.305] [0.188] [0.011] [0.019] [0.011]

On Leave -0.0213 -0.109 0.0819 0.001 0.013 0.002

[0.230] [0.481] [0.251] [0.017] [0.040] [0.016]

Note: All baseline controls included

4.3 Propensity Score Matching

Propensity score matching (PSM) estimation is applied to the low and high maternal

education subsamples. Table 3 displays the results for each category of both PSM and

marginal effects probit models for 3 binary treatment models – full-time employment versus

mother at home, part-time employment versus mother at home and full-time employment

versus mother working part-time.

25

The outcome measure is the probability of having a high SDQ score, and is estimated within

the matching logarithm using marginal effects probit. Results report the treatment effect

on the treated when compared with the counterfactual control group. Consistent with

earlier findings, PSM does not result in any significant effects for children of mothers with

higher levels of educational attainment. However, full-time maternal employment by

mothers with low levels of educational attainment is associated with a higher risk of a child

reporting a high SDQ score when compared to mothers at home5 (PSM: 0.04, Probit (mfx):

0.06) and part-time maternal employment is significant only in the probit model (Probit

0.05). Full-time versus part-time employment by these mothers is not significant under

either estimation.

4.3 Mediation analysis

As maternal employment is significant for children of mothers with low levels of education

only, mediation analysis is applied to this subsample. Table 4 presents results from the

procedure assessing the statistical significance of the natural indirect, natural direct and

marginal total effects of fulltime maternal employment at 9 months on the probability of a

high SDQ score at 3 years. 90% bias-corrected confidence intervals were calculated for each

effect. The marginal total effect is significant at the trend level, while neither the indirect or

5 Effect sizes are consistent under multiple imputation though full-time employment for the low maternal

education subsample is not significant.

Probit (mfx) PSM Probit (mfx) PSM Probit (mfx) PSM Probit (mfx) PSM Probit (mfx) PSM Probit (mfx) PSM

Fulltime v Home 0.060** 0.040* -0.005 -0.011

[0.029] [0.021] [0.013] [0.014]

Parttime v Home 0.051* 0.017 -0.008 -0.014

[0.027] [0.021] [0.014] [0.014]

Full v Part 0.016 0.03 -0.003 0

[0.024] [0.020] [0.011] [0.011]

Covariates:

TABLE 3 - PROPENSITY SCORE MATCHING - PROBABILITY OF HIGH SDQ SCORE (>=14)

LOW MATERNAL EDUCATION HIGH MATERNAL EDUCATION

Full set of baseline controls included in analysis plus maternal and paternal employment at 3 years

26

direct effect is significant. It is also possible to calculate the proportion of the effect of full-

time maternal employment on the probability of a high SDQ score mediated by childcare by

dividing the marginal total effect coefficient by the natural indirect effect coefficient. In

total, 51% of the total effect of full-time maternal employment on the probability of a high

SDQ score was mediated by non-parental childcare at 9 months.

TABLE 4 - MEDIATION ANALYSIS - LOW MATERNAL EDUCATION

OUTCOME: PROBABILITY OF HIGH SDQ SCORE (>=14)

CHILDCARE AS MEDIATOR FOR EFFECT OF MATERNAL EMPLOYMENT Childcare

Fulltime v Home & Mediator Path A 1.328***

[0.038]

Mediator Path B 0.0142

[0.0114]

Fulltime v Home (no mediator) Path C 0.0372*

[0.022]

Fulltime v Home (with mediator) Path C' 0.0184

[0.0269]

Sobel-Goodman: Percentage of total effect mediated 51%

Covariates:

Sample weights not applied to sgmediation analysis in STATA.

Full set of baseline controls included in analysis, plus maternal and paternal employment at 3 years.

Measures of income and parental stress were also tested to investigate if they had a

mediating role between maternal employment and a high SDQ score, and no mediating

effects were found. These finding are consistent with research from the US (Brooks-Gunn et

al., 2010; Lombardi and Coley, 2014). A modest and weak mediating role was found for

quality of mother-child attachment, suggesting the effect of maternal employment on non-

cognitive development may be channelled in some small way through attachment. These

results are detailed in Appendix 5.

27

4.5 The role of Childcare

TABLE 5 - CHILDCARE BY TYPE

PROBABILITY OF SDQ SCORE >=14 (PROBIT)

ALL LOW MATERNAL

EDUCATION HIGH MATERNAL

EDUCATION

N 8,852 3,692 5,160

Childcare at 9 months (base: At home with parent)

Informal Unpaid 0.03 0.02 0.04

[0.031] [0.046] [0.045]

Informal Paid -0.03** -0.02 -0.03***

[0.013] [0.029] [0.01]

Grandparent Unpaid 0.03 0.07* 0.00

[0.021] [0.038] [0.0167]

Grandparent Paid 0.00 0.00 0.00

[0.018 [0.035] [0.016]

Centre Based Care -0.02 0.01 -0.02**

[0.014] [0.036] [0.011]

Childcare at 3 years (base: At home with parent)

Informal Unpaid 0.04 0.07 0.01

[0.042] [0.069] [0.0385]

Informal Paid 0.03 0.06 0.01

[0.017] [0.038] [0.014]

Grandparent Unpaid -0.03* -0.048* 0.00

[0.017] [0.029] [0.019]

Grandparent Paid -0.02 -0.04 0.00

[0.018] [0.030] [0.019]

Centre Based Care 0.00 0.02 -0.01

[0.011] [0.02] [0.010]

Note: All baseline controls included plus maternal employment at 9 months and 3 years

To better understand the mediating role of childcare for children of mothers with low levels

of education, a categorical variable of paid/unpaid childcare by type of care is used. The

results of this probit regression are detailed in Table 5, with unpaid grandparental care

increasing the risk of a high SDQ score by 7 percent. 44.5 percent of children in childcare

within this low maternal education category are cared for by a grandparent, 57.5 percent of

whom are unpaid. If paid childcare can be viewed as a proxy for quality, it would appear

28

that unpaid grandparental care when a child is 9 months old is detrimental to the non-

cognitive development of young children. However, as grandparent care at 3 years of age

reduces the risk of a high SDQ score, this suggests that the first year is a sensitive period for

the development of socio-emotional skills in early childhood.

4.6 Selection on Unobservables

Altonji et al. (2005) propose a theory that uses the degree of selection on observables as a

measure of the degree of selection on unobservables, and provide a method to

quantitatively assess the degree of omitted variable bias. A measurement of the amount of

selection on observables is used in the calculation of a ratio that determines how large the

selection on unobservables would need to be in order to attribute the entire effect of

maternal employment to selection bias6.

Applying this methodology to the current study, a negative bias for the effect of full-time

maternal employment by less well educated mothers of 0.68 is estimated. This implies that

maternal employment is negatively related to as a result of the negative correlation

between maternal employment and the observable determinants of behavioural problems.

The coefficient on full-time maternal employment should therefore be viewed as a lower

bound, such that maternal employment is likely to increase the risk of a high SDQ score by

at least the effect estimated in these results. Ruhm (2008) similarly concludes that, once a

particularly comprehensive number of controls for non-random selection into maternal

employment have been included, remaining omitted variable bias may lead to

underestimates of the adverse effects of maternal employment.

6 For a detailed description refer to Appendix 3

29

5. DISCUSSION

These results suggest that children of employed mothers from less advantaged

backgrounds, as measured by maternal education, have an increased risk of socio-emotional

problems in early childhood, as indicated by the elevated risk of a high SDQ score. Much of

this effect is mediated by childcare, in particular the use of unpaid grandparental care at 9

months. Consistent with the theory of the technology of skill formation which states that

capabilities are produced by investments, the environment, and genes (Heckman et al.,

2007), many of these families may be unable to invest in quality childcare, resulting in a sub-

optimal environment for child development during this sensitive period. However, maternal

employment measured concurrently with the outcome at 3 years does appear to have a

beneficial effect for children within this category, suggesting that the first year is a sensitive

period for non-cognitive development and that the timing of maternal employment does

matter.

While these findings are consistent much of the international literature (Jacob, 2009; Belsky,

2001; NICHD ECCRN, 2003; Gupta and Simonsen, 2010), they may be somewhat explained

by the institutional context of employment and childcare in Ireland. Female employment

rates between 1998 and 2015 increased by 25% and certain policy initiatives have been

introduced over this time period to support maternal employment. In particular, mothers in

employment prior to the birth of a child are entitled to state sponsored maternity benefit

for 26 weeks subject to certain conditions, with the option of a further 16 weeks of unpaid

leave. Some employers at their own discretion, particularly professional and large

organisations, pay top-up payments to maintain salary levels throughout this period.

However, this substantial benefit is largely restricted to the higher educated mothers,

30

allowing them to maintain their financial resources through this period and to maximise the

value of their maternity leave. These women are also likely to benefit from job protection

while on leave. Mothers with lower education levels are less likely to benefit from such

security, with 26% of working mothers in this category returning to work by the time their

child is 5 months old compared with 17% of mothers with higher levels of education. The

majority of higher educated mothers return to employment during or on the expiration of

their unpaid leave.

Despite the rise in female employment, policy initiatives have yet to be introduced to

ensure equal access to affordable childcare. While some subsidised community childcare

places are available to those on very low income, formal childcare in Ireland is largely

privatised and expensive (OECD, 2014), such that families from lower SES backgrounds have

more limited childcare options in the first year when compared with their better resourced

well educated counterparts, and are more reliant on unpaid childcare, in particular care

provided by grandparents. 22% of mothers in the GUI study with low levels of maternal

education state that their choice of childcare is determined by financial constraints,

compared to 12% of mothers with higher levels of education. Consequently, many children

from such resource-constrained backgrounds do not benefit from the structured care of

qualified professionals in formal settings. Childcare accessibility may also limit access to

employment for many of these mothers, with 11% of mothers with low education levels

stating that difficulty in arranging childcare has prevented them from looking for a job (5%

for the high education category) and 8% state they have turned down or left a job due to

such difficulties (also 5% for the high education category).

31

This paper is subject to some limitations due to data availability. Like most studies in this

field, childcare quality is unmeasured and information on the work status of mothers is

limited. Despite these limitations, this study makes a valuable contribution to the

international literature for a number of key reasons. Firstly, mediation analysis improves the

understanding of the relative roles of maternal employment and childcare, while also clearly

illustrating that income and stress are not mechanisms through which the effects of

maternal employment on non-cognitive development are mediated. This analysis also

shows that the quality of the parent-child relationship plays a modest role as a mediator.

The use of propensity score matching which estimates results consist with the initial probit

analysis, allows potential selection bias to be minimised. The application of the

methodology to assess selection bias derived by Altonji et al. (2005) suggests that the

results for maternal employment should be viewed as a lower bound estimate. Finally, as

GUI data relates to children born in 2007/2008, these findings reflect current working and

childcare experiences.

This research concludes that maternal employment and childcare choices have adverse

implications for the non-cognitive development of children from less advantaged

backgrounds, as measured by maternal employment in early childhood. However, there is

no evidence that maternal employment by well educated mothers has an adverse effect on

children at this early stage of child development. Policies that narrow the gap for families

from less advantaged backgrounds should be considered.

32

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35

APPENDIX 1- DETAILED DESCRIPTIVES

DESCRIPTIVE STATISTICS SPLIT BY MOTHER'S EMPLOYMENT STATUS AT 9 MONTHS

ALL HOME PART-TIME FULL-TIME ON LEAVE

N 9751 3802 1994 2650 1272

% 39% 20% 27% 13%

SDQ score 7.79 8.31 7.71 7.35 7.24

SDQ score >=14 12% 14% 11% 9% 9%

Potential Mediators

Child Care at 9 months

At home with Mother 60% 95% 30% 18% 87%

Informal 15% 2% 28% 29% 6%

Grandparent 14% 2% 28% 26% 4%

Formal 11% 2% 15% 27% 4%

Childcare paid at 9 months 31% 3% 50% 68% 9%

Childcare hours at 9 months 10.61 0.70 14.00 26.41 2.26

Child Care at 3 years

At home with Mother 49% 72% 39% 27% 40%

Informal 15% 5% 20% 24% 18%

Grandparent 9% 3% 14% 14% 9%

Formal 27% 20% 28% 35% 33%

Childcare hours at 3 years 12.9 5.5 13.4 21.9 15.6

Childcarepaid at 3 years 45% 24% 52% 65% 54%

Equivalised Household Income at 9 months 21,839 16,309 22,215 27,491 25,624

Maternal Quality of Attachment 9 months 42.55 42.78 42.55 42.17 42.68

Maternal stress at 9 months 14.61 14.98 14.33 14.30 14.57

Equivalised Household Income at 3 years 18,334 14,408 18,644 22,121 21,522

Parent child relationship at 3 years - Positive score 33.80 33.72 33.81 33.88 33.86

Parent child relationship at 3 years - Conflict score 15.60 15.96 15.57 15.17 15.16

Maternal stress at 9 months 12.35 12.72 12.19 12.31 12.13

Workstatus at 3 years

At Home 42% 77% 20% 13% 31%

Part-time 28% 14% 59% 23% 34%

Full-time 23% 6% 15% 54% 23%

Maternity leave 6% 2% 7% 10% 11%

Child & Birth Characteristics

Mother Unemployed at 9 months 3% 8% 0% 0% 0%

Study Child Female 49% 50% 49% 49% 49%

Study child is non-singleton 3% 4% 3% 2% 4%

Study child was preterm 6% 7% 5% 6% 9%

Caesarean Section 26% 24% 26% 27% 28%

Child in poor health at birth 3% 4% 2% 3% 4%

Child in poor health at 9 months 1% 1% 1% 1% 1%

Child temperament scores (9 months)

fussy 14.83 15.25 14.80 14.39 14.51

unadaptable 8.97 9.37 8.85 8.53 8.86

dull 5.85 5.80 5.83 5.86 5.96

unpredictable 6.15 6.14 6.12 6.15 6.21

Maternal Characteristics

Non-Irish Ethnicity 19% 26% 14% 15% 12%

Age at first pregnancy 27.2 25.6 27.4 28.2 29.3

Age when study child is 9 months 31.9 31.3 32.2 31.8 33.5

Maternal Education

Up to leaving Certificate 43% 60% 41% 28% 29%

Degree Level 38% 30% 41% 44% 44%

Postgraduate 19% 10% 18% 28% 27%

36

ALL HOME PART-TIME FULL-TIME ON LEAVE

Chronic illness (Mother) 11% 15% 9% 8% 12%

Mother ever depressed 16% 20% 14% 13% 14%

Mother worked before pregnancy 78% 52% 99% 97% 88%

Mother's workhours before pregnancy 29.4 21.2 32.3 38.1 32.0

Maternal poverty (Age 16) 20% 23% 19% 18% 16%

Family Characteristics

No. of siblings at 9 months 0.99 1.28 0.96 0.63 0.90

Father's Workstatus at 9 months

Working 72% 61% 75% 80% 80%

Unemployed 7% 10% 5% 6% 4%

Missing 21% 29% 19% 14% 16%

Father's Workstatus at 3 years

Working 66% 55% 70% 76% 75%

Unemployed 11% 15% 9% 8% 7%

Missing 23% 30% 21% 17% 17%

Father's Education

Up to leaving Certificate 40% 40% 42% 41% 34%

Degree Level 26% 21% 25% 30% 31%

Postgraduate 13% 10% 13% 15% 20%

Missing 21% 29% 19% 14% 16%

Household Class

Never worked 10% 23% 1% 4% 0%

Unskilled & Semi-skilled 9% 15% 8% 5% 5%

Skilled & Non-manual 30% 32% 35% 24% 27%

Professional/Managerial 51% 30% 56% 68% 68%

Partner 89% 83% 14% 94% 94%

Local Authority Housing 8% 13% 6% 3% 3%

In receipt of Social Welfare 21% 33% 18% 9% 14%

Neighbourhood Deprivation

Low 45% 43% 46% 49% 43%

Medium 48% 47% 49% 47% 52%

High 7% 10% 6% 4% 5%

Urban 43% 45% 40% 43% 47%

Marriage Quality Score 2.87 3.03 2.75 2.80 2.73

Has good support 72% 64% 78% 79% 74%

Family live nearby 64% 61% 70% 65% 62%

Living with Grandparents 3% 3% 4% 4% 2%

English/Irish household language 94% 90% 95% 96% 97%

Mother smoked while pregnant 16% 22% 15% 12% 12%

Mother drank alcohol while pregnant 21% 18% 22% 23% 25%

Mother took drugs while pregnant 2% 2% 2% 1% 1%

37

APPENDIX 2 – FULL REGRESSIONS

OUTCOME: BASE REGRESSION PLUS CHILDCARE 9 MONTHS PLUS CHILDCARE 3 YEARS

SDQ SCORE>=14 ALL LOW HIGH ALL LOW HIGH ALL LOW HIGH

Workstatus at 9 months (v. at home)

Part-time 0.0154 0.0391 -0.00755 0.0163 0.0272 0.000957 0.0154 0.0295 -0.000759

[0.0133] [0.0246] [0.0117] [0.0152] [0.0276] [0.0137] [0.0152] [0.0278] [0.0134]

Full-time 0.0154 0.0505* -0.00804 0.0236 0.0442 0.00455 0.0232 0.0441 0.00320

[0.0134] [0.0276] [0.0117] [0.0169] [0.0338] [0.0149] [0.0168] [0.0336] [0.0148]

Maternity leave -0.00149 0.00632 -0.0116 -0.00203 0.00472 -0.0115 -0.00206 0.00445 -0.0114

[0.0136] [0.0263] [0.0121] [0.0134] [0.0260] [0.0119] [0.0134] [0.0257] [0.0119]

Childcare at 9 months (v. at home with mother)

Informal 0.0175 0.0414 -0.00619 0.0111 0.0268 -0.00859

[0.0230] [0.0438] [0.0196] [0.0223] [0.0416] [0.0193]

Grandparent 0.0290 0.0481 0.0100 0.0374 0.0646 0.00951

[0.0219] [0.0419] [0.0190] [0.0231] [0.0436] [0.0194]

Formal 0.0222 0.0864 -0.0134 0.0249 0.0731 -0.00848

[0.0272] [0.0637] [0.0192] [0.0279] [0.0626] [0.0204]

Childcare hours at 9 months -0.000176 -0.000151 1.25e-05 -0.000123 -9.38e-05 7.02e-05

[0.000538] [0.00115] [0.000452] [0.000540] [0.00111] [0.000469]

Childcare paid at 9 months -0.0314** -0.0455* -0.0166 -0.0344** -0.0489** -0.0177

Workstatus at 3 years (v. at home) [0.0145] [0.0250] [0.0156] [0.0144] [0.0249] [0.0158]

Part-time -0.0216** -0.0347** -0.00701 -0.0209** -0.0336* -0.00676 -0.0220** -0.0384* -0.00612

[0.00990] [0.0177] [0.00981] [0.00986] [0.0176] [0.00972] [0.0111] [0.0199] [0.0107]

Full-time -0.0271** -0.0632*** -0.00113 -0.0264** -0.0635*** -4.28e-05 -0.0255** -0.0700*** 0.00418

[0.0108] [0.0191] [0.0110] [0.0107] [0.0189] [0.0109] [0.0129] [0.0211] [0.0134]

Maternity leave 0.000904 0.0129 0.00192 0.00240 0.0173 0.00270 0.00152 0.0165 0.00336

[0.0174] [0.0399] [0.0156] [0.0175] [0.0410] [0.0156] [0.0174] [0.0407] [0.0156]

Childcare at 3 years (v. at home with mother)

Informal 0.0331 0.0461 0.0190

[0.0278] [0.0521] [0.0256]

Grandparent -0.0166 -0.0556* 0.00920

[0.0189] [0.0308] [0.0211]

Formal 0.00608 0.0153 -0.00112

[0.0225] [0.0412] [0.0215]

Childcare hours at 9 months -0.000345 0.000571 -0.000516

[0.000539] [0.00113] [0.000477]

Childcare paid at 9 months 0.00374 -0.00248 0.00302

[0.0181] [0.0306] [0.0181]

Unemployed Mum at 9 months 0.0264 0.0615 -0.0136 0.0284 0.0627 -0.0114 0.0271 0.0601 -0.0126

[0.0238] [0.0415] [0.0176] [0.0240] [0.0417] [0.0179] [0.0237] [0.0411] [0.0175]

Maternal Stress at 9 months 0.00275*** 0.00382*** 0.00182*** 0.00279*** 0.00391*** 0.00181*** 0.00277*** 0.00386*** 0.00186***

[0.000647] [0.00112] [0.000639] [0.000644] [0.00112] [0.000629] [0.000643] [0.00111] [0.000627]

Quality of Attachment at 9 months -0.00130 0.00186 -0.00340** -0.00141 0.00188 -0.00380*** -0.00145 0.00194 -0.00374***

[0.00154] [0.00283] [0.00147] [0.00154] [0.00283] [0.00146] [0.00153] [0.00282] [0.00144]

Ethnicity 0.0194 0.0309 0.0128 0.0175 0.0308 0.00913 0.0175 0.0290 0.00914

[0.0132] [0.0256] [0.0130] [0.0131] [0.0257] [0.0125] [0.0130] [0.0254] [0.0125]

Mothers age when first pregnant -0.00247* -0.00200 -0.00275** -0.00231* -0.00195 -0.00255** -0.00234* -0.00194 -0.00260**

[0.00129] [0.00222] [0.00114] [0.00127] [0.00218] [0.00113] [0.00127] [0.00217] [0.00113]

Mothers age when child 9 months -0.000432 -0.000708 -0.000199 -0.000330 -0.000547 -0.000154 -0.000371 -0.000712 -2.63e-05

[0.00135] [0.00223] [0.00124] [0.00135] [0.00222] [0.00123] [0.00134] [0.00221] [0.00123]

Maternal Education (v. up to leaving cert)

Degree Level -0.0215** 0.00542 -0.0210** -0.0211**

[0.00864] [0.00837] [0.00863] [0.00861]

Postgraduate -0.0266** -0.0249** -0.00394 -0.0255** -0.00313

[0.0114] [0.0114] [0.00829] [0.0114] [0.00830]

Mother - Chronic illness 0.0152 0.00894 0.0234* 0.0153 0.00834 0.0227* 0.0155 0.00813 0.0235*

[0.0121] [0.0203] [0.0136] [0.0121] [0.0203] [0.0135] [0.0121] [0.0201] [0.0135]

Mother ever depressed 0.0789*** 0.105*** 0.0621*** 0.0783*** 0.103*** 0.0620*** 0.0787*** 0.103*** 0.0628***

[0.0128] [0.0207] [0.0145] [0.0127] [0.0206] [0.0143] [0.0127] [0.0204] [0.0143]

38

OUTCOME: BASE REGRESSION PLUS CHILDCARE PAID PLUS CHILDCARE 3 YEARS

SDQ SCORE>=14 ALL LOW HIGH ALL LOW HIGH ALL LOW HIGH

No of siblings at 9 months -0.0150** -0.0128 -0.0187*** -0.0148** -0.0123 -0.0183*** -0.0149** -0.0116 -0.0189***

[0.00586] [0.00985] [0.00544] [0.00584] [0.00976] [0.00536] [0.00584] [0.00974] [0.00538]

Father's Workstatus at 9 months (v. working)

Unemployed 0.0212 0.0477* -0.0222 0.0198 0.0479* -0.0242* 0.0203 0.0472* -0.0242*

[0.0177] [0.0285] [0.0137] [0.0175] [0.0286] [0.0129] [0.0175] [0.0282] [0.0129]

Missing -0.0297 0.0500 -0.237*** -0.0266 0.0536 -0.235*** -0.0281 0.0505 -0.234***

[0.0763] [0.122] [0.0115] [0.0752] [0.121] [0.0113] [0.0755] [0.125] [0.0113]

Father's Workstatus at 9 months (v. working)

Unemployed 0.0241 0.0198 0.0297 0.0237 0.0195 0.0276 0.0242 0.0188 0.0264

[0.0149] [0.0235] [0.0182] [0.0148] [0.0234] [0.0178] [0.0149] [0.0235] [0.0178]

Missing 0.0314** 0.0523** 0.00932 0.0321** 0.0528** 0.00941 0.0308** 0.0491** 0.00989

[0.0129] [0.0221] [0.0128] [0.0129] [0.0222] [0.0126] [0.0129] [0.0221] [0.0126]

Paternal Education (v. up to leaving cert)

Degree Level 0.00184 -0.0124 0.00244 0.00178 -0.0125 0.00295 0.00153 -0.0128 0.00282

[0.0103] [0.0210] [0.00941] [0.0103] [0.0211] [0.00930] [0.0103] [0.0209] [0.00924]

Postgraduate 0.0133 0.0378 0.00480 0.0144 0.0372 0.00705 0.0144 0.0371 0.00786

[0.0154] [0.0463] [0.0125] [0.0154] [0.0463] [0.0125] [0.0154] [0.0459] [0.0126]

Missing 0.0342 -0.0401 0.991*** 0.0291 -0.0446 0.991*** 0.0308 -0.0406 0.991***

[0.101] [0.103] [0.000777] [0.0961] [0.0999] [0.000764] [0.0980] [0.104] [0.000762]

Household social class (v. never worked)

Unskilled & Semi-skilled 0.0123 0.0213 0.00726 0.00779 0.0171 0.00312 0.00729 0.0155 0.00286

[0.0217] [0.0317] [0.0322] [0.0210] [0.0311] [0.0303] [0.0208] [0.0308] [0.0300]

Skilled & Non-manual -0.00652 -0.00191 -0.00808 -0.0100 -0.00511 -0.0107 -0.0111 -0.00786 -0.0110

[0.0183] [0.0281] [0.0242] [0.0180] [0.0280] [0.0233] [0.0179] [0.0277] [0.0231]

Professional/Managerial -0.0383* -0.0398 -0.0339 -0.0417** -0.0425 -0.0374 -0.0427** -0.0453 -0.0374

[0.0200] [0.0288] [0.0310] [0.0199] [0.0284] [0.0311] [0.0198] [0.0280] [0.0309]

Living with Partner -0.0336 -0.0447 -0.0126 -0.0315 -0.0427 -0.0111 -0.0307 -0.0367 -0.0123

[0.0260] [0.0408] [0.0283] [0.0256] [0.0404] [0.0273] [0.0254] [0.0393] [0.0277]

Study child Female -0.0317*** -0.0461*** -0.0198*** -0.0320*** -0.0469*** -0.0203*** -0.0308*** -0.0442*** -0.0200***

[0.00765] [0.0140] [0.00731] [0.00762] [0.0139] [0.00723] [0.00757] [0.0138] [0.00718]

Study child is non-singleton 0.0240 0.0177 0.0272 0.0238 0.0176 0.0272 0.0255 0.0218 0.0276

[0.0247] [0.0427] [0.0255] [0.0246] [0.0426] [0.0253] [0.0249] [0.0430] [0.0254]

Study child was preterm 0.0173 0.0231 0.0130 0.0167 0.0235 0.0134 0.0173 0.0257 0.0135

[0.0181] [0.0317] [0.0178] [0.0180] [0.0318] [0.0175] [0.0181] [0.0320] [0.0175]

Caesarean Section 0.00834 0.0141 0.00246 0.00802 0.0139 0.00191 0.00810 0.0135 0.00185

[0.00910] [0.0168] [0.00849] [0.00904] [0.0167] [0.00836] [0.00900] [0.0166] [0.00831]

Child in poor health at birth 0.0288 0.0518 0.0109 0.0264 0.0483 0.00951 0.0277 0.0548 0.00973

[0.0240] [0.0422] [0.0255] [0.0236] [0.0417] [0.0247] [0.0239] [0.0430] [0.0247]

Child in poor health at 9 months -0.0203 -0.0216 -0.0199 -0.0201 -0.0254 -0.0169 -0.0199 -0.0291 -0.0162

[0.0287] [0.0643] [0.0230] [0.0286] [0.0615] [0.0241] [0.0283] [0.0581] [0.0246]

Local Authority Housing 0.00434 -0.000396 0.00794 0.00365 -0.00198 0.00851 0.00309 -0.00414 0.00818

[0.0151] [0.0213] [0.0256] [0.0149] [0.0210] [0.0255] [0.0148] [0.0208] [0.0256]

In receipt of Social Welfare 0.00106 -0.00767 0.0190 0.000726 -0.00715 0.0177 0.00129 -0.00554 0.0176

[0.0101] [0.0160] [0.0131] [0.0100] [0.0159] [0.0128] [0.0100] [0.0159] [0.0128]

Neighbourhood Deprivation (v. Low)

Medium 0.0108 0.0163 0.00447 0.00973 0.0147 0.00366 0.00955 0.0140 0.00367

[0.00816] [0.0152] [0.00771] [0.00812] [0.0152] [0.00764] [0.00809] [0.0151] [0.00761]

High 0.0404** 0.0583** 0.0122 0.0391** 0.0575* 0.0119 0.0387** 0.0552* 0.0127

[0.0192] [0.0297] [0.0211] [0.0190] [0.0296] [0.0209] [0.0189] [0.0293] [0.0211]

Urban -0.00591 -0.00455 -0.00599 -0.00687 -0.00585 -0.00642 -0.00733 -0.00989 -0.00506

[0.00804] [0.0145] [0.00771] [0.00800] [0.0144] [0.00766] [0.00804] [0.0144] [0.00774]

Mother worked before pregnancy 0.0123 0.000694 0.0373*** 0.0118 0.00123 0.0360*** 0.0120 0.000743 0.0355***

[0.0112] [0.0185] [0.0119] [0.0112] [0.0184] [0.0120] [0.0111] [0.0184] [0.0120]

Mother's workhours before pregnancy -9.42e-05 -4.06e-05 -0.000566 -8.68e-05 -2.98e-05 -0.000518 -8.39e-05 -2.45e-05 -0.000478

[0.000115] [0.000148] [0.000449] [0.000110] [0.000144] [0.000447] [0.000108] [0.000142] [0.000446]

Maternal poverty (Age 16) 0.00718 0.0127 0.00236 0.00719 0.0118 0.00222 0.00755 0.0118 0.00218

[0.00961] [0.0162] [0.00963] [0.00957] [0.0161] [0.00952] [0.00955] [0.0160] [0.00945]

39

OUTCOME: BASE REGRESSION PLUS CHILDCARE PAID PLUS CHILDCARE 3 YEARS

SDQ SCORE>=14 ALL LOW HIGH ALL LOW HIGH ALL LOW HIGH

Marriage Quality Score -0.0114*** -0.0139** -0.00866*** -0.0116*** -0.0145** -0.00863*** -0.0113*** -0.0136** -0.00861***

[0.00352] [0.00656] [0.00330] [0.00350] [0.00653] [0.00327] [0.00350] [0.00650] [0.00326]

Has good support -0.00254 0.0108 -0.0103 -0.00510 0.00749 -0.0127 -0.00453 0.00873 -0.0123

[0.00921] [0.0162] [0.00931] [0.00936] [0.0164] [0.00948] [0.00932] [0.0162] [0.00951]

Family live nearby 0.00645 0.0215 -0.00374 0.00602 0.0211 -0.00400 0.00631 0.0212 -0.00444

[0.00860] [0.0157] [0.00826] [0.00859] [0.0157] [0.00820] [0.00857] [0.0156] [0.00818]

Living with Grandparents -0.00963 -0.0288 0.0100 -0.0110 -0.0300 0.00775 -0.00949 -0.0273 0.00796

[0.0242] [0.0353] [0.0323] [0.0239] [0.0352] [0.0308] [0.0239] [0.0352] [0.0306]

English/Irish household language -0.0199 -0.0283 -0.0158 -0.0191 -0.0285 -0.0146 -0.0190 -0.0262 -0.0144

[0.0207] [0.0375] [0.0218] [0.0206] [0.0376] [0.0212] [0.0205] [0.0368] [0.0212]

Child temperament scores (9 months)

fussy 0.00332*** 0.00419*** 0.00244*** 0.00331*** 0.00420*** 0.00235*** 0.00337*** 0.00431*** 0.00243***

[0.000883] [0.00153] [0.000903] [0.000883] [0.00153] [0.000891] [0.000882] [0.00153] [0.000884]

unadaptable 0.000126 -0.000674 0.00100 6.98e-05 -0.000596 0.000891 1.18e-05 -0.000654 0.000793

[0.00109] [0.00190] [0.00109] [0.00108] [0.00189] [0.00108] [0.00108] [0.00188] [0.00108]

dull 0.000592 -0.00309 0.00318* 0.000687 -0.00313 0.00335** 0.000601 -0.00325 0.00330**

[0.00166] [0.00299] [0.00163] [0.00166] [0.00300] [0.00161] [0.00165] [0.00299] [0.00161]

unpredictable 0.00562*** 0.0105*** 0.00101 0.00558*** 0.0105*** 0.000905 0.00559*** 0.0109*** 0.000902

[0.00148] [0.00256] [0.00157] [0.00148] [0.00255] [0.00155] [0.00148] [0.00255] [0.00155]

Mother smoked while pregnant 0.00803 0.0104 0.00851 0.00930 0.0139 0.00796 0.0102 0.0161 0.00808

[0.0108] [0.0168] [0.0135] [0.0108] [0.0168] [0.0133] [0.0108] [0.0168] [0.0132]

Mother drank alcohol while pregnant 0.00300 -0.0212 0.0194** 0.00426 -0.0205 0.0209** 0.00484 -0.0207 0.0214**

[0.00961] [0.0177] [0.00950] [0.00967] [0.0178] [0.00953] [0.00967] [0.0176] [0.00950]

Mother took drugs while pregnant 0.00875 0.0244 -0.0127 0.00777 0.0230 -0.0128 0.00698 0.0206 -0.0135

[0.0305] [0.0511] [0.0274] [0.0301] [0.0506] [0.0273] [0.0298] [0.0498] [0.0268]

Observations 8,858 3,695 5,163 8,857 3,695 5,162 8,852 3,692 5,160

Robust standard errors in brackets *** p<0.01, ** p<0.05, * p<0.1

40

APPENDIX 3 – SELECTION BIAS

The Problem

In order to identify a causal effect of maternal employment when a child is 9 months on the

probability of a child having a high SDQ score at 3 years of age, the coefficient on the regressor

variable must not contain, either partly or entirely, the effect of relevant characteristics not

identified and controlled for in the estimation. While sufficient controls should identify the effect of

observables, it may prove more challenging to identify the existence of unobserved characteristics

that impact the relationship between the explanatory variable and the outcome and, if appropriate,

adjust the explanatory variable to exclude the influence of unobserved characteristics. In the

absence of an appropriate instrumental variable for maternal employment, an estimation method

developed by Altonji et al., (2005) is used to assess selectivity bias.

Potential Solution - Altonji Methodology

Selection Bias

Adapting the approach taken in Altonji, Elder and Taber (2005) and taking maternal employment as

our endogenous variable, the outcome (Y), representing the probability of the study child having a

high SDQ score, is determined by:

Y* = αME + W’Ϯ Equation (1)

= αME + X + ҽ Equation (2)

ME is a binary variable that represents 1 if the mother works and α is the causal effect of maternal

employment on the risk of a high SDQ score. W represents a vector of observed and unobserved

variables that determine Y*, and Ϯ is the causal effect of this vector of variables on the outcome. X is

a vector of observable characteristics of W, and is the causal effect of this sub-vector of W. The

error component, ҽ, is an index of the unobservable variables. As we cannot control for these

41

unobservables, to the extent that they are correlated with both ME, the explanatory variable, and

the outcome, Y*, the estimation results may be biased.

Theoretical Foundation

Altonji et al. (2005) propose a theory that uses the degree of selection on observables as a measure

of the extent of selection on unobservables, and provide a method to quantitatively assess the

degree of omitted variable bias. A measurement of the amount of selection on observables is used

in the calculation of a ratio that determines how large the selection on unobservables would need to

be in order to attribute the entire effect of either maternal employment or childcare to selection

bias.

This methodology relies on 3 key assumptions, which are required to derive Condition 1:

1. The variables in X, the observed variables, are chosen at random from the full set or

variables W that determine Y;

2. The number of variables in both X and W are large, such that no one element dominates the

distribution of ME or Y;

3. The regression of ME* on Y*- αME is equal to the regression of the part of ME* that is

orthogonal to X on the corresponding part of Y* - αME. ME* is the latent variable that

determines ME such that ME=1(ME*>0), where the indicator function 1(.) is 1 when ME*>0

and zero otherwise. ME* is therefore exogenous. The authors propose that this assumption

is weaker than the standard OLS assumption of Cov (X, ҽ).

These assumptions allow the authors to set selection on the unobservables equal to selection on

observables. What this means is that the part of Y* that is related to the observables and the part

related to the unobservables have the same relationship with ME*. This is known as Condition 1.

42

Condition 2 says that the part of Y* that relates to the unobservables has no relationship with ME*.

While this is a standard assumption in econometrics, it’s unlikely to hold in practice, as many of the

factors that influence Y* are correlated with maternal employment or X.

The authors, in the context of discussing the effect of attending a Catholic School (CH) on

educational attainment and test scores, comment that the “random selection on observables”

assumption required as part of Condition 1 should not be taken literally. They suggest there are

compelling reasons why the relationship between the unobservables and CH (or, in this case ME) is

likely to be weaker than the relationship between the observables and CH. Applying their thoughts

to this study, the reasons why this might be so are:

1. The selection of the covariates is not random, such that they have been selected in order to

reduce bias. For example, maternal education and household class are both related to ME

and child behavioural problems.

2. Ҽ is also likely to contain a random element of child overweight, perhaps traits of the child or

mother that are not related to the decision of a mother to work.

3. Shocks that occur after 9 months are not included within the regressors. These shocks may

influence the SDQ score of the child but not the decision to return to work when the child is 9

months.

The final condition, Condition 3, involves the authors identifying a set of bounds for α. The upper

bound occurs with the assumption that Cov (ME*, ҽ)/Var (ҽ) = 0 and a lower bound that assumes

=

Equation (3)

By arguing that for the decision of a mother to work, selection on unobservables is likely to be less

strong than selection on observables. By estimating joint models of maternal employment and the

outcome, the SDQ score of the child, subject to selection on unobservables and observables being

43

equal, we achieve this lower bound estimate. Both OLS and Probit assume no selection on

unobservables, and therefore provide an upper bound estimate.

Should the sign of the estimated effect of the unobservables on the outcome be negative, this would

alter this logic, such that the bounds as outlined above would be reversed, with Cov (ME*, ҽ)/Var (ҽ)

= 0 providing a lower bound estimate. This logic means that the unobservable factors that influence

a mother’s decision to work may have a favourable impact on the child risk of a high SDQ score. Such

factors may include a diligent well organised mother or an even tempered child.

Application of Altonji et al. Methodology

The first step of this estimation involves finding an estimate of Ϯ under the null hypothesis of no

maternal employment effect:

= α + Ϯ + Equation (4)

This equation provides estimates of , and , as indentified in

Equation (3) above. Using these 3 estimates, an estimate of the implied bias, can be

computed. A measure of the strength of this implied bias is determined from its ratio to the

estimate of β, representing how strong selection on unobservables would have to be relative to

selection on observables in order to attribute the entire estimated effect of maternal employment

to selection bias (Elder & Jepsen, 2014).

The Results

Column 1 of Table A2.1 details the OLS estimates of the binary treatment on the total sample, and

the sample split by maternal education. Column 3 details the level of selection bias if selection on

observables is set equal to selection on unobservables, and Column 4 lists the implied ratio.

This study obtains effects for full-time maternal employment for children of mothers with low levels

of maternal education. While the small implied ratio suggests that the absolute effect of the

44

unobservables would only need to be 8% as strong as the unobservables to explain the OLS

estimate, the fact that the bias and therefore the implied ratio are negative suggests that the OLS

estimate should be viewed as a lower bound. Therefore, the existence of selection bias is likely to

understate the true effect of full-time maternal employment for this subsample.

TABLE A3.1

Estimates of bias of the effects of Maternal Employment based on the Altonji et al. Methodology (Limited Probability Model)

OUTCOME: Probability of High SDQ score at 3 years of age

Treatment Sample OLS Estimate Significance Estimated Bias Implied Ratio

(1) (2) (3) (4)

Full-time Employment v Home All 0.03 No -1.23 -0.02

Full-time Employment v Home High Maternal Education only -0.01 No -0.59 0.02

Full-time Employment v Home Low Maternal Education only 0.05 10% -0.68 -0.08

Part-time Employment v Home All 0.01 No -0.69 -0.02

Part-time Employment v Home High Maternal Education only -0.01 No -0.46 0.03

Part-time Employment v Home Low Maternal Education only 0.04 No -0.38 -0.09

Note 1: Beta: coefficient on binary treatment with full controls, child's BMI as outcome measure, population weights applied and no imputation

Note 2: As estimated bias is negative, selection on unobservables would have to be of the opposite sign to selection on observables for true effect of maternal

employment to be zero. Therefore, effect of maternal employment on increasing risk of a High SDQ score may be understated.

Interpretation of Results

The application of this methodology to the results in the paper suggests that the effect of full-time

maternal employment by mothers with relatively lower levels of education on the risk of a child

having a high SDQ score may be understated, such that unobservable factors, be they characteristics

of the mother or the child, offset some of the effect of maternal employment.

45

APPENDIX 4 - PROPENSITY SCORE MATCHING

Choice of Matching Estimator, Selection of Variables for PSM estimation & Bias Reduction

Propensity score matching was used on three configurations of maternal employment, as

detailed by Table 4. However, in order to ensure the most appropriate matching estimator

is applied, a number of estimators were tested, using full-time maternal employment as the

treatment and Mother at Home as the counterfactual.

Variables that are not affected by participation in the treatment (Caliendo and Kopeinig,

2005) are used in the estimation of the propensity score. These variables are then evaluated

to assess the quality of the matching process before MI, with a maximum difference

between the two groups of 5% deemed acceptable.

Propensity scores were estimated using a probit model and three types of matching

methods were assessed. The radius-caliper method matches each treatment child to all

children in the control group with an estimated propensity score within a particular caliper

(distance). As this method matches treatment observations with controls within the

specified caliper, is allows for usage of extra units when good matches are available, thus

oversampling and avoiding the risk of bad matches. A possible problem with this method is

that it’s difficult to determine a priori what tolerance level is reasonable (Smith & Todd,

2005). For this reason 3 difference calipers were applied (0.01, 0.001, 0.1) and results from

each were broadly consistent, though the bias reduction was smallest for the largest caliper.

The second method applied was nearest neighbour (NN) matching, with the treatment child

matched with the child in the control group with the nearest estimated propensity score.

This method was initially applied with no replacement, which produced the most limited

46

reduction in bias, such that the method was deemed inappropriate. This method of

matching is sensitive to the order in which matching occurs and while it may reduce

variance, it does tend to lead to a higher bias. 3 formulations of nearest neighbour matching

were then applied with replacement, firstly matching with replacement to the single nearest

neighbour, then to the nearest 5 and 10 control observations using a uniform weight. All 3

versions of NN matching with replacement produced satisfactory reductions in bias levels.

The final matching estimator, the kernel density estimator, matches each student to a

weighted average of all observations in the comparison group, with each observation in the

comparison group weighted inversely proportional to the difference between the

observations estimated propensity score and the propensity score of the treatment child.

While this methodology results in a lower variance as more information is used (Caliendo &

Kopeinig, 2005), this can be at the expense of bad matches. 6 versions of the estimator are

applied, the first simply applying the kernel distribution and the second the normal

distribution, both giving satisfactory results. However, as the match should be within the

area of common support, the remaining third version imposes this condition, as does the

fourth, while also imposing a normal distribution, again giving similar results. Finally, 2

bandwidths are applied in the fifth and sixth version of 0.01 and 0.001 respectively, with

results identical to the fourth estimation, such that there is no sensitivity to the imposition

of the limit of a bandwidth.

Based on its comparability to most estimators and its success in reducing bias, radius-caliper

matching with a calliper of 0.01 was selected to perform all matching. Equivalised family

income and childcare are excluded from the estimation of the propensity score as they are

believed to be endogenous to maternal employment.

47

TABLE A4.1 PROPENSITY SCORE MATCHING - ASSESSMENT OF QUALITY OF ESTIMATORS

UNMATCHED % BIAS

0.01 0.1 0.001

1 5 10 Kernel Normal

Normal &

Common

Support

Kernel

Normal &

Common

Support

Normal,

Common

Supoprt

BW 0.01

Normal,

Common

Supoprt

BW 0.001

Maternal Ethnicity -16.7 -2.2 -2.3 1.7 -8.8 -1.9 -1.3 -1.5 -1.7 -1.9 -1.7 -2 -2 -2

Maternal Chronic Illness -25.1 0.1 -1.2 3.8 -6.7 4.5 -3.5 -2.7 -0.03 4.5 -0.3 4.6 4.6 4.6

Household Class 73.5 -1.2 5.2 -2.3 32.7 -10.2 -4 -2.4 0.1 -10.2 0.1 -10.4 -10.4 -10.4

No if siblings at 9 months -64.9 5.8 0.2 5 -9 0.1 6.4 7.1 3.2 0.1 3.4 0.1 0.1 0.1

Gender (Female) -2.3 2.1 -0.7 4.6 -4.9 2.6 2.8 1.6 -1.6 2.6 -0.9 5.6 5.6 5.6

Non-singleton -10.0 -13 -2.9 -4.8 -4.9 -4.1 0.2 0.2 -2.2 -4.1 -2.3 -4.2 -4.2 -4.2

Pre-term -0.3 -6.9 -7.5 -6.2 -2.2 -4.9 -5.4 -7.9 -6.3 -4.9 -8.5 -7.9 -7.9 -7.9

C Section 10.0 3.4 4.5 0.5 4.6 3 5.9 5.6 3.2 3 4.1 6.4 6.4 6.4

Child health at birth -2.8 -1.6 -2.5 -4.4 -3 -6 -3.9 -2.4 -2.1 -6 -2.1 -6.1 -6.1 -6.1

Child health at 9 months -7.1 -2.6 -4.2 1.5 1.7 1.7 -4 -5.9 -5.9 1.7 -6 1.7 1.7 1.7

Social Welfare -58.7 -1.5 -4.4 -0.6 -19.1 -1.7 -0.5 -1.9 -2.4 -1.7 -2.4 -1.7 -1.7 -1.7

Area Deprevation -24.5 -1.3 -1.9 -0.1 -7 0.2 -1.5 -3.2 -1.6 0.2 -0.8 -0.9 -0.9 -0.9

Urban -3.7 -1.1 1.3 1.3 2.6 -2.9 -2.3 -1.5 0 -2.9 0.1 -0.9 -0.9 -0.9

Mother worked before birth 113.8 6.1 8.8 7.8 11.8 6.8 6.5 6.3 6.8 6.8 7 7 7 7

Mothers work hours before birth 49.8 -0.3 -0.9 6.6 11.9 1.3 -4 -7.4 -7.2 1.3 -7.2 1.2 1.2 1.2

Maternal Poverty age 16 -16.6 5.8 4.9 2.3 -1 6.1 6.3 3.5 6.1 6.1 6 5.9 5.9 5.9

Sufficient support 40.2 -0.3 1.6 1.4 14.2 1.7 -0.6 -0.9 -0.2 1.7 -0.2 1.7 1.7 1.7

Family nearby 15.1 7 7.5 -1.3 6.9 10.7 9.9 7.8 7.6 10.7 7.7 11.6 11.6 11.6

English/Irish household language 12.3 -0.6 0.5 -3.8 8.4 -1.8 -1.2 0.8 0.3 60 0.3 -1.9 -1.9 -1.9

Temperament

Fussy -19.6 2.1 0 3.5 -9.6 -2.4 0.1 1.6 1.8 -2.4 2 -0.6 -0.6 -0.6

Unadaptable -21.0 -1.3 -3.6 1.4 -11.8 -5.2 -5.5 -1.9 -1.4 -5.2 -1.5 -3.1 -3.1 -3.1

Dull 3.8 2.7 0.5 4 1 1.1 6 3.4 2.9 1.1 0.9 -0.1 -0.1 -0.1

Unpredictable 7.3 -4.1 -1.9 -1.2 -3.4 -7 -3.5 -0.5 -0.6 -7 -1.1 -8.3 -8.3 -8.3

Mother smoked while pregnant -21.4 3 0.3 2.6 -4.6 4.6 2 2.9 1.4 4.6 1.9 4 4 4

Mother drank while pregnant 3.5 3.6 5.1 4.3 0 -1.2 6.9 3.4 5.3 -1.2 4.8 -2.4 -2.4 -2.4

Mother took drugs while pregnant -4.0 1.8 1.4 2.1 0 2.1 -1.5 1.3 1.5 2.1 0 2.2 2.2 2.2

MEAN BIAS 2.7 2.9 3 7.4 3.7 3.7 3.3 2.8 3.7 2.9 3.9 3.9 3.9

RADIUS CALIPER NEAREST NEIGHBOUR KERNAL

No

replacement

Replacement

48

APPENDIX 5 – MEDIATION ANALYSIS

FULL MEDIATION ANALYSIS - LOW MATERNAL EDUCATION

OUTCOME: PROBABILITY OF HIGH SDQ SCORE (>=14)

Childcare Income Stress

Quality of

Attachment

Fulltime v Home & Mediator Path A 1.328*** 0.48*** -0.247 -0.769***

[0.038] [0.060] [0.369] [0.142]

Mediator Path B 0.0142 -0.002 0.005 -0.004

[0.0114] [0.008] [0.001] [0.003]

Fulltime v Home (no mediator) Path C 0.0372* 0.041* 0.036* 0.040*

[0.022] [0.023] [0.023] [0.022]

Fulltime v Home (with mediator) Path C' 0.0184 0.042* 0.037* 0.037*

[0.0269] [0.024] [0.022] [0.022]

Sobel-Goodman: Percentage of total effect mediated 51% -2% -3% 7%

Covariates:

Sample weights not applied to sgmediation analysis in STATA.

POTENTIAL MEDIATORS

Full set of baseline controls included in analysis, plus maternal and paternal employment at 3 years.